Sheikh Ahmed, who is also Kuwait's Minister of Defence, was received at Zabeel Palace.
Earlier, Sheikh Mohammed met Sheikh Ahmad at Dubai International Airport, where they exchanged cordial greetings.
At Zabeel Palace, they discussed bilateral relations and ways in which to strengthen historical ties between the UAE and Kuwait.
Sheikh Mohammed and Sheikh Ahmad also exchanged views on a number of regional and international issues of mutual interest.
Sheikh Ahmed bin Mohammed, Second Deputy Ruler of Dubai and Chairman of the Dubai Media Council, also met Sheikh Ahmad Fahd.
The meeting was also attended by Sheikh Ahmed bin Saeed, president of the Dubai Civil Aviation Authority and chairman and chief executive of Emirates Airline and Group, and a number of sheikhs, ministers and senior officials.